A duality for symmetric spaces with applications to group representations

1970/08/01 by Sigurdur Helgason, Sigurđur Helgason · 251 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebra over a field #Duality (order theory) #Geometry and complex manifolds #Group (periodic table) #Group representation #Mathematics #Pure mathematics

paper · pdf · doi:10.1016/0001-8708(70)90037-x

published in Advances in Mathematics 5(1), 1-154 (Elsevier BV)

crossref issued 1970/08/01 · crossref published 1970/08/01 · crossref published-print 1970/08/01 · openalex publication_date 1970/08/01 · crossref created 2004/12/19 · crossref deposited 2019/01/30 · openalex created_date 2025/10/10 · crossref indexed 2026/07/18 · openalex updated_date 2026/08/02

Citations

• Discrete series for semisimple Lie groups I: Construction of invariant eigendistributions
• On the existence and irreducibility of certain series of representations
• On a Differential-Geometric Method in the Theory of Analytic Stacks
• Sur les représentations unitaires des groupes de Lorentz généralisés
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• Spherical Functions on a Semisimple Lie Group, I

Cited by

• Remarks on classical invariant theory
• The spherical Fourier transform of rapidly decreasing functions. A simple proof of a characterization due to Harish-Chandra, Helgason, Trombi, and Varadarajan
• The Fourier transform of Harisch-Chandra's c-function and inversion of the Abel transform
• A quick proof of Harish-Chandra’s Plancherel theorem for spherical functions on a semisimple Lie group
• Some Conjectures for Root Systems
• Multipliers and a Paley-Wiener Theorem for Real Reductive Groups
• Plancherel theorem for spherical functions [wikipedia]